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Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
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Bootstrap for Mean with 95% Confidence Interval

I've been working through a book Modern Data Science with R and I have a conceptual question about bootstrapping and confidence intervals. Say you do a bootstrap for a mean 1000 times. How do you get the 95% confidence interval? According to the…
Gandalf_the_Green
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What is a 'critical value' in statistics?

Here's where I encountered this word: The raw material needed for the manufacture of medicine has to be at least $97\%$ pure. A buyer analyzes the nullhypothesis, that the proportion is $\mu_0=97\%$, with the alternative hypothesis that the…
JohnPhteven
  • 2,007
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One-sided confidence interval for variance

I am little bit confused about how we get the upper bound for CI for variance: We have $\frac{(n-1) s^2}{\sigma^{2}}\sim X^2(n-1)$ $$P\left(\frac{(n-1)s^2}{\sigma^{2}}>X^2_{1-\alpha,n-1}\right)=1-\alpha$$ and if we solve for $\sigma^{2}$ then we…
F.O
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CDF of $\max(x_1,x_2)+\max(x_3,x_4)$ where all $x_i$s are iid from $U[a,b]$

I am looking for the cumulative density function of the sum of two variables, which are themselves the result of a rank order process. Thus, if $x_1, x_2, x_3$ and $x_4$ are all independent draws from a uniform distribution with support $[a,b]$,…
user58641
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Determine the type of the correlation

If the equation of the regression line of y on x is $$y=3-x$$ Then the correlation between x and y is // (inverse , perfect inverse )? Does the coeffecient of x means the correlation in perfect as it equals -1 ?.
Hussien Mohamed
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Using variance properties to find the standard deviation of a sample

The question is: The standard deviation of the mean mass of a sample of 2 aubergines is 20 g smaller than the standard deviation in the mass of a single aubergine. Find the standard deviation of the mass of an aubergine. So, I chose X as the mass…
minnn
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Can anyone shed some light on the below statistical theory questions?

Can anyone shed some light on the below: Consider a set with $N$ distinct members, and a function $f$ defined on $\mathbb Q$ that takes the values $0$, $1$ such that $\frac1N\sum_{x\in\mathbb Q} f(x) = p$. For a subset $S$ of $\mathbb Q$ of size…
SilvaSquarred
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moment of iid sums

Let Let $X_1,X_2,X_3,X_4$ be a sequence of independent, identically distributed random variables with: $$ E(X) = 0 $$ $$ E(X^2)=1$$ $$E(X^3) = 1$$ $$E(X^4) = 6 $$ Let: $$S_1 =X_1$$ $$S_2 =X_1+X_2$$ $$S_3 = X_1+X_2+X_3$$ and so on. Show that…
Rito Lowe
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How to see wether numbers are distributed "evenly" ([1,2,18,35,36]) or "cluttered to one side" ([1,2,3,30,31], [7,9,17,16,36])?

I have a set of 5 integer numbers {1,23, 17, 33, 35}. Elements can take values only from [1..36], and happen only once within the set. What math can I use to understand, wether the numbers are distributed "evenly" (means very symmetric with respect…
caasdads
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Log Likelihood vs Chi Squared- what's the difference?

A program I have used for a linguistics analysis offers the option of using log likelihood or chi-squared to calculate the keyness of a word (Keyness being the actual frequency of a word in a text in comparison to the expected frequency based upon…
Eloisa
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How Does Probability Recursion Work?

I don't undstand how the textbook come up with recursive forumulas. For example, Consider the following gambling game for two players, Black and White. Black puts $b$ black balls and White puts $w$ white balls in a box. Black and White take turns…
A_for_ Abacus
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How to find the MLE of multiple parameters

Suppose $X_1,\ldots,X_n,Y_1,\ldots,Y_n$ are independent exponential r.v., where the density of $X_i$ is $f_i(x)= \lambda_i\theta \exp(-\lambda_i \theta x_i)$ for $x\geq0$, while the density of $Y_i$ is $g_i(x) = \lambda_i \exp(-\lambda_i x_i)$ for…
MGF01
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Compute a measure of "near multiplicity" from a list of noisy values

Question I posted this question on StackOverflow before but someone advised me to ask it there because it looks like a numerical algorithm problem. Let us say I've got a list of values which have a common multiple greater than 1. For example, let us…
snoob dogg
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Probability question involving a dice

You roll a dice $6$ times. What is the probability of rolling at least one $5$ AND at least one $6$? The answer in the book is $1 - (5/6)^6 - (5/6)^6 + (4/6)^6$. Would someone please explain why that is? $(1 - (5/6)^6 - (5/6)^6)$ : This is the…
Quaxton Hale
  • 1,258
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Generate a random pair of integers whose product is less than or equal to x?

Ideally, the distribution over the acceptable pairs would be close to uniform. x and the pair are all positive integers (This is for code, so I need a constructive solution) Thanks!
Garrett Andersen
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